Who was the first to consider that categories were semi-simplicial sets (and in particular groupoids were simplicial sets)?
I think there was a concept of nerve of a covering in algebraic topology before (maybe Alexandroff).
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Sign up to join this communityWho was the first to consider that categories were semi-simplicial sets (and in particular groupoids were simplicial sets)?
I think there was a concept of nerve of a covering in algebraic topology before (maybe Alexandroff).
In Peter Johnstone's 1977 "Topos theory" (p.48) the simplicial description of categories is attributed to Grothendieck and he cites the "Technique de la descente"-series of Bourbaki seminars 1959-62 for it. I guess what he has in mind is in particular prop.4.1 on page 108 of the third installment Préschémas quotients from 1961.